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National and Regional Contests
Netherlands Contests
Dutch Mathematical Olympiad
2004 Dutch Mathematical Olympiad
1
1
Part of
2004 Dutch Mathematical Olympiad
Problems
(1)
lcm (a, b) = 2004
Source: Dutch NMO 2004 p1
9/21/2019
Determine the number of pairs of positive integers
(
a
,
b
)
(a, b)
(
a
,
b
)
, with
a
≤
b
a \le b
a
≤
b
, for which lcm
(
a
,
b
)
=
2004
(a, b) = 2004
(
a
,
b
)
=
2004
. lcm (
a
,
b
a, b
a
,
b
) means the least common multiple of
a
a
a
and
b
b
b
. Example: lcm
(
18
,
24
)
=
72
(18, 24) = 72
(
18
,
24
)
=
72
.
number theory
least common multiple